Common bean (Phaseolus vulgaris L.) is sensitive to different types of abiotic stresses (drought, high temperature, low soil fertility, and acid soil), and this may limit its adaptation and consequently to its yield under stress. Because of this, a sister species, tepary bean (Phaseolus acutifolius A. Gray), has recently gained attention in breeding for improved abiotic stress tolerance in common bean. In this study, we evaluated the adaptation of 302 accessions of tepary bean (Phaseolus acutifolius A. Gray) and its wild relatives (grouped in four types of tepary bean genetic resource: cultivated, acutifolius regressive, acutifolius wild, tenuifolius wild) when grown under high temperature and acid soil conditions with aluminum toxicity in the Amazon region of Colombia. Our objective was to determine differences among four types of tepary bean genetic resource in their morpho-phenological, agronomic, and physiological responses to combined high temperature and acid soil stress conditions. We found that cultivated P. acutifolius var acutifolius presented a greater number of pods per plant, as well as larger seeds and a greater number of seeds per pod. Some traits, such as root biomass, days to flowering and physiological maturity, specific leaf area, and stomatal density, showed significant differences between types of tepary bean genetic resource, probably contributing to difference in adaptation to combined stress conditions of high temperature and acid soil conditions. The photochemical quenching (qP) was higher in cultivated P. acutifolius var. acutifolius, while energy dissipation by non-photochemical quenching (NPQ) in the form of heat and the coefficient of non-photochemical dissipation (qN) were higher in acutifolius regressive and tenuifolius wild accessions. We have identified 6 accessions of cultivated and 19 accessions of tenuifolius wild that exhibited grain yields above 1800 kg ha−1. These accessions could be suitable to use as parents to improve dry seed production of tepary bean under combined stress conditions of high temperature and acid soil.